Until now, we have obtained all coupling constants involving in our calculation. However, there exists the phenomenological parameter \(\alpha _\Lambda \)  introduced in Eq. (REF ) to parametrize the cutoff \(\Lambda \) . Since the cutoff \(\Lambda \)  should not deviate from the physical mass of the exchanged meson, \(\alpha _\Lambda \)  is restricted to be of the order of unity [1]}.
Since there does not exist direct experimental data to constrain the \(\alpha _{\Lambda }\)  value, we have to borrow the experience of the \(\Upsilon (10860)\)  transition into \(\Upsilon _J(1D)\eta \)  [2]}As higher states above the \(B\bar{B}\)  threshold, the \(\Upsilon (10753)\)  is close to the \(\Upsilon (10860)\) , where these two states have similar widths [3]}., where the branching ratio of \(\Upsilon (10860)\rightarrow \Upsilon _J(1D)\eta \)  is of the order of magnitude of \(10^{-3}\) .
To reach up to this order of magnitude,
we should take the range \(0.2\le \alpha _\Lambda \le 0.4\) , which
satisfies the requirement of \(\alpha _\Lambda \)  [1]}.
For the \(\Upsilon (10753)\rightarrow \Upsilon (1^3D_J)\eta \)  (\(J=1,2,3\) ) processes, the \(\alpha _{\Lambda }\)  dependence of the discussed branching ratios is displayed in left panel of Fig. REF .
